Question 1175842
{{{ highlight(11cm)}}}<br>

The workout:
Let {{{s[1]}}} and {{{s[2]}}} be the side lengths of the two squares<br>

Start with two equations
{{{ 4s[1] + 4s[2] = 68 }}} --->  {{{ s[1] + s[2] = 17 }}}
{{{ s[1]^2 + s[2]^2 = 157 }}}<br>

From here, substitute {{{s[1] = 17-s[2]}}} from the top eqn into the bottom:

{{{ (17-s[2])^2 + s[2]^2 = 157 }}} 
Simplify, and factor
{{{ 2s[2]^2 -34s[2] + 132 = 0 }}}
{{{ s[2]^2 - 17s[2] + 66 = 0 }}}
{{{ (s[2]-11)(s[2]-6) = 0 }}}

So {{{ s[2] = 11 }}}  -->  {{{ s[1] = 6 }}}
or {{{ s[2] = 6 }}}   -->  {{{ s[1] = 11}}}   <<< same answer, {{{s[1]}}} is simply the larger square for this solution

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Check:  4*11 + 4*6 = 44 + 24 = 68
       11^2 + 6^2 = 121 + 36 = 157